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1. The equation of a plane parallel to the xy-plane is

A. z = c B. x = c C. y = c D. x + y + z = 0

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2. The distance of the point (2, 3, 4) from the origin is

A. sqrt(29) B. sqrt(14) C. 5 D. 7

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3. The equation of a sphere with center (1, -2, 3) and radius 5 is

A. (x-1)^2 + (y+2)^2 + (z-3)^2 = 25 B. (x+1)^2 + (y-2)^2 + (z+3)^2 = 25 C. (x-1)^2 - (y+2)^2 + (z-3)^2 = 25 D. (x-1)^2 + (y-2)^2 - (z+3)^2 = 25

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4. The shortest distance between the lines x/1 = y/2 = z/3 and x/2 = (y+1)/3 = (z-1)/4 is

A. sqrt(14)/7 B. sqrt(11)/7 C. sqrt(13)/7 D. sqrt(9)/7

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5. The direction cosines of a line are given by

A. l^2 + m^2 + n^2 = 1 B. l + m + n = 1 C. l^2 - m^2 + n^2 = 1 D. l^2 + m^2 + n^2 = 0

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6. The equation of the plane passing through (1, 2, 3) and perpendicular to the vector (4, -5, 6) is

A. 4(x-1) - 5(y-2) + 6(z-3) = 0 B. 4(x+1) + 5(y-2) - 6(z+3) = 0 C. x + y + z = 0 D. x - y + z = 0

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7. The angle between the planes x + y + z = 1 and 2x - 3y + 4z = 5 is

A. cos^-1(1/sqrt(21)) B. sin^-1(1/sqrt(21)) C. tan^-1(1/sqrt(21)) D. cos^-1(1/2)

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8. The distance of the point (1, -1, 2) from the plane 3x + 2y - 2z + 5 = 0 is

A. 2/sqrt(17) B. 3/sqrt(17) C. 4/sqrt(17) D. 5/sqrt(17)

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9. The parametric equations of a line passing through (3, -2, 5) and parallel to (1, 4, -6) are

A. x = 3 + t, y = -2 + 4t, z = 5 - 6t B. x = 3 - t, y = -2 - 4t, z = 5 + 6t C. x = 3 + t, y = -2 - 4t, z = 5 + 6t D. x = 3 - t, y = -2 + 4t, z = 5 - 6t

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10. The vector equation of the plane passing through the point (2, -3, 5) and normal to the vector (1, 1, -2) is

A. r·(i + j - 2k) = 6 B. r·(i - j + 2k) = 6 C. r·(i + j + 2k) = 6 D. r·(i - j - 2k) = 6

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11. The length of the perpendicular from the point (1, 2, 3) to the plane x - y + z = 5 is

A. 2/sqrt(3) B. 3/sqrt(3) C. 4/sqrt(3) D. 5/sqrt(3)

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12. The equation of the plane passing through (1, 0, 0), (0, 1, 0), and (0, 0, 1) is

A. x + y + z = 1 B. x - y + z = 1 C. x + y - z = 0 D. x - y - z = 1

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13. The line x = 2 + t, y = 3t, z = 1 - t intersects the plane x + y + z = 7 at

A. t = 2 B. t = 1 C. t = 3 D. t = 4

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14. The equation of the sphere with center (1, -1, 2) and radius 3 is

A. (x-1)^2 + (y+1)^2 + (z-2)^2 = 9 B. (x+1)^2 + (y-1)^2 + (z+2)^2 = 9 C. (x-1)^2 - (y+1)^2 + (z-2)^2 = 9 D. (x+1)^2 + (y+1)^2 - (z-2)^2 = 9

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15. The angle between the lines with direction ratios (1, 2, 3) and (4, -5, 6) is

A. cos^-1(1/3) B. sin^-1(1/3) C. tan^-1(1/3) D. cos^-1(2/3)

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16. The coordinates of the centroid of a tetrahedron with vertices (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1) are

A. (1/4, 1/4, 1/4) B. (1/3, 1/3, 1/3) C. (1/2, 1/2, 1/2) D. (1, 1, 1)

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17. The volume of a tetrahedron with vertices (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1) is

A. 1/6 B. 1/3 C. 1/2 D. 1

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18. The equation of the line passing through (3, -2, 5) and parallel to (2, -1, 4) is

A. (x-3)/2 = (y+2)/-1 = (z-5)/4 B. (x+3)/2 = (y-2)/-1 = (z+5)/4 C. (x-3)/-2 = (y+2)/1 = (z-5)/-4 D. (x-3)/2 = (y-2)/1 = (z+5)/-4

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19. The shortest distance between the lines x/1 = y/2 = z/3 and (x-1)/2 = (y+1)/3 = (z-2)/4 is

A. sqrt(29)/5 B. sqrt(27)/5 C. sqrt(23)/5 D. sqrt(21)/5

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20. The vector perpendicular to both (1, 2, 3) and (4, 5, 6) is

A. (-3, 6, -3) B. (3, -6, 3) C. (6, -3, 6) D. (-6, 3, -6)